ME 565: Mechanical Engineering Analysis (Winter 2015, University of Washington). Instructor: Professor Steven Brunton. Complex analysis. Partial differential equations. Transform methods (Laplace and Fourier transforms).
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This course will provide an in-depth overview of powerful mathematical techniques for the analysis of engineering systems. In addition to developing core analytical capabilities, students will gain proficiency with various computational approaches used to solve these problems. Applications will be emphasized, including fluid mechanics, elasticity and vibrations, weather and climate systems, epidemiology, space mission design, and applications in control. (from washington.edu)
Course Currilcum
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- Lecture 01 – Complex Numbers and Functions Unlimited
- Lecture 02 – Roots of Unity, Branch Cuts, Analytic Functions, and the Cauchy-Riemann Conditions Unlimited
- Lecture 03 – Integration in the Complex Plane (Cauchy-Goursat Integral Theorem) Unlimited
- Lecture 04 – Cauchy’s Integral Formula Unlimited
- Lecture 05 – ML Bounds and Examples of Complex Integration Unlimited
- Lecture 06 – Inverse Laplace Transform and the Bromwich Integral Unlimited
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- Lecture 07 – Canonical Linear PDEs: Wave Equation, Heat Equation, and Laplace’s Equation Unlimited
- Lecture 08 – Heat Equation: Derivation and Equilibrium Solution in 1D (i.e., Laplace’s Equation) Unlimited
- Lecture 09 – Heat Equation in 2D and 3D, 2D Laplace Equation (on Rectangle) Unlimited
- Lecture 10 – Analytic Solution to Laplace’s Equation in 2D (on Rectangle) Unlimited
- Lecture 11 – Numerical Solution to Laplace’s Equation in Matlab, Intro to Fourier Series Unlimited
- Lecture 12 – Fourier Series Unlimited
- Lecture 13 – Infinite Dimensional Function Spaces and Fourier Series Unlimited
- Lecture 14 – Fourier Transforms Unlimited
- Lecture 15 – Properties of Fourier Transforms and Examples Unlimited
- Lecture 16 – Discrete Fourier Transforms (DFT) Unlimited
- Lecture 17 – Fast Fourier Transforms (FFT) and Audio Unlimited
- Lecture 18 – FFT and Image Compression Unlimited
- Lecture 19 – Fourier Transform to Solve PDEs: 1D Heat Equation on Infinite Domain Unlimited
- Lecture 20 – Numerical Solutions to PDEs Using FFT Unlimited
- Lecture 21 – The Laplace Transform Unlimited
- Lecture 22 – Laplace Transform and ODEs Unlimited
- Lecture 23 – Laplace Transform and ODEs with Forcing and Transfer Functions Unlimited
- Lecture 24 – Convolution Integrals, Impulse and Step Responses Unlimited
- Lecture 25 – Laplace Transform Solutions to PDEs Unlimited
- Lecture 26 – Solving PDEs in Matlab using FFT Unlimited
- Lecture 27 – Singular Value Decomposition (SVD) and Data Science 1 Unlimited
- Lecture 28 – Singular Value Decomposition (SVD) and Data Science 2 Unlimited
- Lecture 29 – Singular Value Decomposition (SVD) and Data Science 3 Unlimited
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